Wow, that sounds like a silly question, but really! My wife froze bananas in the freezer with the peel still on. You can't peel them frozen. I put it in the microwave for one minute at 50% power. After 30 seconds the thin end of the peel (where a bunch connect to each other) was on fire, with a visible flame (about the size of a lighter). What on earth happened?
It's caused by the high amount of potassium in the banana. Microwaves react with metals, bouncing off and cause arcing. You can even create a cool light show by putting a raw peeled banana in the microwave. Don't worry, it won't explode, but it will make a mess, it's also harmless.
This can also happen in some frozen vegetables depending on the soil conditions they grew in. As noted in the linked article, other high concentrations of metals such as magnesium, iron, and zinc can be the responsible mineral.
Momentary brief sparking is harmless and won't harm your microwave, but the USDA recommends turning off your microwave if you see sparks nonetheless. If it does start a fire, unless it's a very small fire, do not open your microwave door. The safest thing is to turn off the microwave and let the fire burn itself out by consuming all the oxygen. Opening the door could create a dangerous backdraft induced fireball.
This may also be related to the dielectric antenna effects that cause grapes to spark in a microwave :
I found that single grapes would eject steam out of the stem hole forming little rocket engines which often propelled the grapes about the oven. If the stem was left in the grape, so that the steam could not escape, the grape skin would quickly rupture in a small explosion as it was heated.
There are two general classes of antennas, metallic conducting antennas and dielectric antennas that concentrate electromagnetic fields. The common antennas most people are familiar with are antennas made from conducting wires and rods such as the rabbit ears on indoor TV antennas or the multirod TV antennas on millions of roof tops. Dielectric antennas include various geometric solids including cylinders, spheres and plastic focusing lenses.
I keep my bananas in the frig and warm them up (one at a time) in the microwave. It is the stem which burns/smolders/smokes, in as little as 20 seconds. I don't know why, but I think it may have to do with the lack of water.
It could have fermented and alcohol ignited it
Bananas is the only fruit that contains radiation. That is why it will catch fire.
I belive the potassium in the banana would be a good conductor, but I have a few things to add.
The microwave runs on, well microwaves a form of radiation that penitrates what's in there and heats from with in. A banana is also slightly radioactive, not harmful to humans though, and I belive the potassium is a conductor of both the microwaves and the radioactivity of the banana reacting to one another and the potassium is then chemically changed and then reacts to the microwaves emitted from the device That's my hypothesis anyway let me know what you think.